Preface

This booklet has been adapted for inclusion in the Educational
Practices Series developed by the International Academy of Education (IAE) and
distributed by the International Bureau of Education (IBE) and the Academy. As
part of its mission, the Academy provides timely syntheses of research on
educational topics of international importance. This booklet is the fourth in
the series on educational practices that generally improve learning.

The material was originally prepared for the Handbook of
research on improving student achievement, edited by Gordon Cawelti and
published in a second edition in 1999 by the Educational Research Service (ERS).
The Handbook, which also includes chapters on subjects such as generic practices
and science, is available from ERS (2000 Clarendon Boulevard, Arlington, VA
22201-2908, United States of America; phone (1) 800-791-9308; fax (1)
800-791-9309; and website: www.ers.org).

ERS is a not-for-profit research foundation serving the research
and information needs of educational leaders and the public. Established in
1973, ERS is sponsored by seven organizations: the American Association of
School Administrators; the American Association of School Personnel
Administrators; the Association of School Business Officials; the Council of
Chief State School Officers; the National Association of Elementary School
Principals; the National Association of Secondary School Principals; and the
National School Public Relations Association. As Vice-President of the Academy
and editor of the present series, I thank ERS officials for allowing the IAE and
the IBE to make available the material adapted from the Handbook to
educators around the world.

The first author of the present pamphlet, Douglas A. Grouws, is
Professor of Mathematics Education at the University of Iowa. He was the editor
of the Handbook of research on mathematics teaching and learning
(Macmillan, 1992) and has a large number of other publications on research
in mathematics education to his credit. He has made invited research
presentations in Australia, China, Hungary, Guam, India, Japan, Mexico, Thailand
and the United Kingdom. He has directed several research projects for the
National Science Foundation (NSF) and other agencies in the areas of
mathematical problem-solving and classroom teaching practices. His current NSF
work involves mathematics and technology. He received his Ph.D. from the
University of Wisconsin.

The second author, Kristin J. Cebulla, is a mathematics
education doctoral student at the University of Iowa. She previously taught
middle-school mathematics. Before teaching, she worked as a research chemical
engineer. She received her bachelor of science degree in mathematics and
chemical engineering from the University of Notre Dame and her masters
degree from the University of Mississippi.

The principles described in this booklet are derived in large
part from the United States and other English-speaking countries. Other research
also has important implications for the teaching of mathematics. An example is
Realistic Mathematics Education, initiated by H. Freudenthal and developed since
the early 1970s at the University of Utrecht (Dordrecht, The Netherlands,
Kluwer, 1991). Another example is research on problem-solving summarized in a
recent book by L. Verschaffel, B. Greer, and E. De Corte-Making sense of word
problems (Lisse, The Netherlands, Swets & Zeitlinger, 2000).

The officers of the International Academy of Education are aware
that this booklet is based on research carried out primarily in economically
advanced countries. The booklet, however, focuses on aspects of learning that
appear to be universal in much formal schooling. The practices seem likely to be
generally applicable throughout the world. Even so, the principles should be
assessed with reference to local conditions, and adapted accordingly. In any
educational setting, suggestions or guidelines for practice require sensitive
and sensible application and continuing evaluation.